This paper is dedicated to study the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredohlm integral equations in Banach space, the recent researches considered the study of differential equations of mixed Volterra-Fredholm integral equations with classical order and the study of existence and uniqueness of solutions using approched numerical methodes, the objective of this paper is the study of the existence and uniqueness of fractional order of differential equations with mixed Volterra-Fredholm integral equations using fixed point theory. This work have two important results, the first result was the discussion of the existence of solutions using the Krasnoselskii fixed point theorem after transforming the problem into integral equation firstly then into operator problem suitable for the fixed point theory. The second result will be the existence and uniqueness of solution, this result was obtained by the use of Banach fixed point theorem after the same transformation used in the first one. This work give as conclusion that the boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredholm integral equation has a unique solution in Banach space. Finally, this work was ended with an example to illustrate the results obtained.
Published in | American Journal of Applied Mathematics (Volume 12, Issue 1) |
DOI | 10.11648/j.ajam.20241201.11 |
Page(s) | 1-8 |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Mixed Volterra-Fredohlm Integral Equation, Existence and Uniqueness, Fixed Point Theory
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APA Style
Taier, A. E., Wu, R., Iqbal, N. (2024). Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space. American Journal of Applied Mathematics, 12(1), 1-8. https://doi.org/10.11648/j.ajam.20241201.11
ACS Style
Taier, A. E.; Wu, R.; Iqbal, N. Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space. Am. J. Appl. Math. 2024, 12(1), 1-8. doi: 10.11648/j.ajam.20241201.11
AMA Style
Taier AE, Wu R, Iqbal N. Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space. Am J Appl Math. 2024;12(1):1-8. doi: 10.11648/j.ajam.20241201.11
@article{10.11648/j.ajam.20241201.11, author = {Ala Eddine Taier and Ranchao Wu and Naveed Iqbal}, title = {Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space}, journal = {American Journal of Applied Mathematics}, volume = {12}, number = {1}, pages = {1-8}, doi = {10.11648/j.ajam.20241201.11}, url = {https://doi.org/10.11648/j.ajam.20241201.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20241201.11}, abstract = {This paper is dedicated to study the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredohlm integral equations in Banach space, the recent researches considered the study of differential equations of mixed Volterra-Fredholm integral equations with classical order and the study of existence and uniqueness of solutions using approched numerical methodes, the objective of this paper is the study of the existence and uniqueness of fractional order of differential equations with mixed Volterra-Fredholm integral equations using fixed point theory. This work have two important results, the first result was the discussion of the existence of solutions using the Krasnoselskii fixed point theorem after transforming the problem into integral equation firstly then into operator problem suitable for the fixed point theory. The second result will be the existence and uniqueness of solution, this result was obtained by the use of Banach fixed point theorem after the same transformation used in the first one. This work give as conclusion that the boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredholm integral equation has a unique solution in Banach space. Finally, this work was ended with an example to illustrate the results obtained.}, year = {2024} }
TY - JOUR T1 - Boundary Value Problem of Nonlinear Fractional Differential Equations of Mixed Volterra-Fredohlm Integral Equations in Banach Space AU - Ala Eddine Taier AU - Ranchao Wu AU - Naveed Iqbal Y1 - 2024/02/28 PY - 2024 N1 - https://doi.org/10.11648/j.ajam.20241201.11 DO - 10.11648/j.ajam.20241201.11 T2 - American Journal of Applied Mathematics JF - American Journal of Applied Mathematics JO - American Journal of Applied Mathematics SP - 1 EP - 8 PB - Science Publishing Group SN - 2330-006X UR - https://doi.org/10.11648/j.ajam.20241201.11 AB - This paper is dedicated to study the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredohlm integral equations in Banach space, the recent researches considered the study of differential equations of mixed Volterra-Fredholm integral equations with classical order and the study of existence and uniqueness of solutions using approched numerical methodes, the objective of this paper is the study of the existence and uniqueness of fractional order of differential equations with mixed Volterra-Fredholm integral equations using fixed point theory. This work have two important results, the first result was the discussion of the existence of solutions using the Krasnoselskii fixed point theorem after transforming the problem into integral equation firstly then into operator problem suitable for the fixed point theory. The second result will be the existence and uniqueness of solution, this result was obtained by the use of Banach fixed point theorem after the same transformation used in the first one. This work give as conclusion that the boundary value problem of nonlinear fractional differential equations of mixed Volterra-Fredholm integral equation has a unique solution in Banach space. Finally, this work was ended with an example to illustrate the results obtained. VL - 12 IS - 1 ER -